We have proved Henon-Lane-Emden conjecture is true for space dimension $N=3$ by scaling invariant of the solutions and Sobolev embedding on $S^{N-1}$. Then we obtained new Liouville-type theorems and showed Henon-Lane-Emden conjecture for polyharmoic system holds in a new region, and also proved the generalized H\'{e}non-Lane-Emden conjecture in $R^2$ and $R^3$. Moreover, we prove some new results on related Schrodinger systems.
